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When one refers to "the" discrete cosine transform (DCT), it is generally assumed that one means the type II DCT, where the input array $x_k$ ($0 \leq k < N-1$) is even about $k=-1/2$ and $k=N-1/2$.

Is there a similar convention for "the" discrete sine transform? MATLAB defaults to type I, while Mathematica prefers type II. The FFTW docs are silent on the matter.

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There are eight kinds of DCTs, and eight kinds of DSTs. The classification is due to Wang and Hunt.

You'd do well to just specify the DTT type explicitly; DCT-II being the "default" DCT is due to its ubiquity (e.g. JPEG). Personally, I tend to use types I, II, and III of DST and DCT in my work, and I think it is not unhelpful to always append the type to the DCT or DST that you're using.

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Just to be painfully explicit. DCT-II is the default because of its ubiquity. However, the DST (all eight of them) has not developed a similar convention. –  matt Dec 7 '11 at 0:20
    
Yep, nice summary. :) –  J. M. Dec 7 '11 at 0:26

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